Question

f(x)=x^2/3 and g(x)=sqrt(x-3)Find (f o g) (x) and (f o g)(4)

Answer 1

SOLUTION:

Step 1 :

We are considering two equations:

$\begin{gathered} f(x)=x^{\frac{2}{3}} \\ \text{and } \\ g\text{ ( x ) = }\sqrt[]{x-3} \end{gathered}$

Step 2:

First, we are meant to find the formula for:

$(f^o\text{g)(x) and then we simplify our answer}$$(f^og)(x)\text{ = f(g(x))}$$\begin{gathered} (f^og)(x)\text{ = f(g(x))} \\ f(\sqrt[]{x-3}\text{ ) } \\ \text{but f ( x ) = x}^{\frac{2}{3}} \\ \text{Then, (f}\sqrt[]{x-3\text{ }})\text{ = (}\sqrt[]{x-3})^{\frac{2}{3}} \\ (f^og)(x\text{ ) = ( }\sqrt[]{x-3})^{\frac{2}{3}} \end{gathered}$

Step 3:

$\begin{gathered} \operatorname{Re}call\text{ that} \\ \\ (f^o\text{g)(x) =(}\sqrt[]{x\text{ - 3}})^{\frac{2}{3}} \\ (f^og)\text{ (4) = (}\sqrt[]{4-3})^{\frac{2}{3}} \\ =1^{\frac{2}{3}} \\ =\text{ 1} \\ \text{CONCLUSION:} \\ (f^og)(4)\text{ = 1} \end{gathered}$